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Universal Coding on Infinite Alphabets: Exponentially Decreasing Envelopes

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1 Author(s)
Dominique Bontemps ; Laboratoire de Mathématiques d'Orsay, Univ Paris-Sud, Orsay

This paper deals with the problem of universal lossless coding on a countable infinite alphabet. It focuses on some classes of sources defined by an envelope condition on the marginal distribution, namely exponentially decreasing envelope classes with exponent . The minimax redundancy of exponentially decreasing envelope classes is proved to be equivalent to . Then, an adaptive algorithm is proposed, whose maximum redundancy is equivalent to the minimax redundancy.

Published in:

IEEE Transactions on Information Theory  (Volume:57 ,  Issue: 3 )